Problem: Wangari plants trees at a constant rate of $12$ trees every $3$ hours. Write an equation that relates $p$, the number of trees Wangari plants, and $h$, the time she spends planting them in hours.
Solution: Let's find the constant of proportionality. In the proportional relationship between $p$, the number of trees Wangari plants, and $h$, the time she spends planting them in hours, one constant of proportionality is the number of trees she plants per hour. It is the number we multiply by the number of hours to get the number of trees she plants. $h\,\times\, ?=p$ $\begin{aligned} h\,\times\, {?}&=p \\\\ {?}&=\dfrac{p}{h} \\\\ &=\dfrac{12}{3} \\\\ &={4} \end{aligned}$ The constant of proportionality is ${4}$. This means we can multiply ${4}$ by the number of hours to get the number of trees. Now, let's write the equation: $\begin{aligned} \text{number of trees}&={\text{planting rate}}\times\text{number of hours} \\\\ p&={4}h \end{aligned}$ One correct equation is: $p = 4h$